TITLE

A smooth global branch of solutions for a semilinear elliptic equation on $${\mathbb{R}^N}$$

AUTHOR(S)
Genoud, Fran�ois
PUB. DATE
May 2010
SOURCE
Calculus of Variations & Partial Differential Equations;May2010, Vol. 38 Issue 1/2, p207
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The existence of a global branch of positive spherically symmetric solutions {(?, u(?)) : ? ? (0,8)} of the semilinear elliptic equation ?u - ?u + V(x)?u?p-1u =0 in RN with N = 3 is proved for 1 < p < 1+ 4-2b/ N-2 , where b ? (0, 2) is such that the radial function V vanishes at infinity like ?x?-b. V is allowed to be singular at the origin but not worse than ?x-b. The mapping ? ? u(?) is of class Cr ((0,8), H1(RN )) if V ? Cr (RN \ {0},R), for r = 0, 1. Further properties of regularity and decay at infinity of solutions are also established. This work is a natural continuation of previous results by Stuart and the author, concerning the existence of a local branch of solutions of the same equation for values of the bifurcation parameter ? in a right neighbourhood of ? = 0. The variational structure of the equation is deeply exploited and the global continuation is obtained via an implicit function theorem.
ACCESSION #
49024221

 

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